{"title":"Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers","authors":"Bishal Deb , Alan D. Sokal","doi":"10.1016/j.aam.2024.102756","DOIUrl":null,"url":null,"abstract":"<div><p>A D-permutation is a permutation of <span><math><mo>[</mo><mn>2</mn><mi>n</mi><mo>]</mo></math></span> satisfying <span><math><mn>2</mn><mi>k</mi><mo>−</mo><mn>1</mn><mo>≤</mo><mi>σ</mi><mo>(</mo><mn>2</mn><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span> and <span><math><mn>2</mn><mi>k</mi><mo>≥</mo><mi>σ</mi><mo>(</mo><mn>2</mn><mi>k</mi><mo>)</mo></math></span> for all <em>k</em>; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.</p></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0196885824000885/pdfft?md5=3810ddd45e6b3ed90210b39501d14be8&pid=1-s2.0-S0196885824000885-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885824000885","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A D-permutation is a permutation of satisfying and for all k; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.
期刊介绍：
Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas.
Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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